Two infinite-area thin planar conducting plates are separated by distance . The

Question

Two infinite-area thin planar conducting plates are separated by distance . The plates have uniform surface charge densities + and , respectively, on their inside surfaces. [Each plate has two surfaces—the inside surface of a plate is nearest the other plate.]

(a) Ignore the negative plate for the moment. Use Gauss’s Law to obtain the electric field at all points in space of the positively charged plate alone. (There are two regions to consider here.)

(b) Now consider both plates. Use the result of part (a) and superposition to obtain the electric field at all points in space. (There are three regions to consider here.)

Explanation / Answer

a] Take a cylinderical Gaussian surface of radius r such that one face of cylinder lies on one side of the plate and other lies on other side.

By Gauss law, Flux = q/e0

E.pi r^2 *2 = * pi r^2 / e0

E =   / 2e0

on left side, field would be leftward and on the right side it would be rightward.

b] on left of the first plate , E = [-]/2e0 = 0

in between the plates E =  [- -]/2e0 = /e0

on right of the second plate, E = [ -]/2e0 = 0

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